The phenomenon of paid search advertising has now become the most predominant form of online advertis-ing in the marketing world. However, we have little understanding of the impact of search engine adver-
tising on consumers’ responses in the presence of organic listings of the same firms. In this paper, we modeland estimate the interrelationship between organic search listings and paid search advertisements. We use aunique panel data set based on aggregate consumer response to several hundred keywords over a three-monthperiod collected from a major nationwide retailer store chain that advertises on Google. In particular, we focuson understanding whether the presence of organic listings on a search engine is associated with a positive,a negative, or no effect on the click-through rates of paid search advertisements, and vice versa for a givenfirm. We first build an integrated model to estimate the relationship between different metrics such as searchvolume, click-through rates, conversion rates, cost per click, and keyword ranks. A hierarchical Bayesian mod-eling framework is used and the model is estimated using Markov chain Monte Carlo methods. Our empiricalfindings suggest that click-throughs on organic listings have a positive interdependence with click-throughson paid listings, and vice versa. We also find that this positive interdependence is asymmetric such that theimpact of organic clicks on increases in utility from paid clicks is 3.5 times stronger than the impact of paidclicks on increases in utility from organic clicks. Using counterfactual experiments, we show that on an aver-age this positive interdependence leads to an increase in expected profits for the firm ranging from 4.2% to6.15% when compared to profits in the absence of this interdependence. To further validate our empirical results,we also conduct and present the results from a controlled field experiment. This experiment shows that totalclick-through rates, conversions rates, and revenues in the presence of both paid and organic search listings aresignificantly higher than those in the absence of paid search advertisements. The results predicted by the econo-metric model are also corroborated in this field experiment, which suggests a causal interpretation to the positiveinterdependence between paid and organic search listings. Given the increased spending on search engine-basedadvertising, our analysis provides critical insights to managers in both traditional and Internet firms.
Key words : paid search advertising; organic search listings; search engines; click-through rates; conversionrates; electronic commerce; Internet markets; monetization of user-generated content; hierarchical Bayesianmodeling
History : Received: February 10, 2008; accepted: October 21, 2009; processed by Alan Montgomery.Published online in Articles in Advance.
1. IntroductionOver the past few years, search engines like Google,Yahoo!, and MSN have discovered that as interme-diaries between consumers and firms, they are in aunique position to sell new forms of advertisements.This has led to the proliferation of sponsored searchadvertising—where advertisers pay a fee to Internetsearch engines to be displayed alongside nonspon-sored or organic Web search results. Because searchengine-based advertising is directly related to users’search queries, it is considered by users as being farless intrusive relative to other forms of online adver-tising. From the firm side, this kind of advertisingleads to more qualified prospects because the adsare displayed in response to user-originated searchbehavior. From the consumer perspective, this is a
much more relevant form of advertising because thekeywords and the ad message are typically matchedwith user-generated queries. These features have leadto a widespread adoption of this form of Web 2.0media by firms, with the global paid search mar-ket expected to reach almost $10 billion by the endof 2009.1
How does this mechanism work? In sponsoredsearch, firms who wish to advertise their productor services on the Internet create text-based ads andsubmit that information in the form of “keyword”listings to search engines. A keyword is a combina-tion of words or terms that best describes the prod-uct, brand, or retailer being advertised. Bid values are
assigned to each individual keyword and then searchengines pit advertisers against each other in second-price auction-style bidding for the highest positionson search engine result pages. When users search forthat keyword on a search engine, the relevant adalong with the advertisers’ Web page appears as asponsored link on the top and the right side of theorganic search results. When users click on the spon-sored ad, they are taken to the advertiser’s website.An important determinant of the effectiveness of
sponsored search advertising for a given advertiser isthe likelihood of the same advertiser appearing in thenatural or organic listings of the search engine, and itsposition on the organic listings for a given keyword.Organic rankings of advertisers’ websites are basedon a complex and proprietary indexing algorithmdevised by the search engine involving the quality ofthe website and the website’s “relative importance”with respect to other links. Thus, consumers often facetwo competing lists of results that may both be rel-evant to their search query: (i) the sponsored searchlisting and (ii) the organic search listing.Advertisers have been grappling with the trade-
offs in each of these two forms of referrals. On theone hand, because a firm can control the messageof paid search ads, one would expect higher conver-sions from them. On the other hand, because peoplevalue the perceived “editorial integrity” of organiclistings, one would expect higher conversions fromthem. Some anecdotal evidence suggests that thereis a potential disconnect between the perception ofsponsored listings by business and users, with con-sumers having a positive bias towards organic searchlistings. For example, Hotchkiss et al. (2005) find thatmore than 77% of participants favored organic linksmore than the sponsored links as offering sources oftrusted, unbiased information. A similar set of find-ings are reported in Greenspan (2004). On the otherhand, Jansen (2007) finds that sponsored links aremore relevant than organic links in the context of e-commerce search queries, and this finding is robustto usage across Google, Yahoo!, and MSN searchengines. Moreover, there is also some anecdotal evi-dence suggesting that paid search may lead to higherconversions than organic search.2 This study looked atsearch engine visits on Google, Yahoo!, and MSN andshowed a median order conversion rate of 3.4% forpaid search compared to a conversion rate of 3.13%for organic search results during the same time frame.These mixed findings then motivate the question
regarding to what extent should firms invest in spon-sored search advertisements when they also appearin the organic listings for a given search query in that
2 See http://www.searchnewz.com/blog/talk/sn-6-20060925OrganicVersusPaidSearchResults.html.
search engine. After all, firms incur costs while engag-ing in paid search advertising. Despite the growth ofsearch advertising, we have little understanding ofthe impact of sponsored search advertising on con-sumers’ overall reaction in the presence of organicsearch listings for a given firm. Our key objectivein this paper is to compare and analyze the interde-pendence between paid ad listings with organic list-ings for a given advertiser. Hence, we focus on thefollowing questions: How do different keyword-levelattributes impact performance metrics such as aver-age click-through rates and conversion rates in paidsearch advertising as compared with those in organicsearch listings? What is the nature of the relationshipbetween average click-through rates on organic andpaid listings for a given set of keywords? Are thecombined click-through rates, conversion rates, andrevenues from sponsored and organic listings higheror lower than those from organic listings only (i.e.,when paid search advertising is paused)?Although an emerging stream of theoretical liter-
ature in sponsored search has looked at issues suchas mechanism design in auctions, no prior work hasempirically analyzed these kinds of questions. Bymodeling the association between paid and organicclicks, we aim to examine if there is a positive, neg-ative, or zero association between them. Towardsthis goal, we use a unique panel data set of aggre-gate consumer response to several hundred keywordsover three months collected from a large nationwideretailer that advertises on Google. To be clear, we onlyhave aggregate keyword-level data, not disaggregateuser-level data. We propose a hierarchical Bayesianmodeling framework in which we model consumers’aggregate responses jointly with the advertiser’s andsearch engine’s decisions. Our paper is the first aca-demic study that estimates the effect of sponsoredsearch advertising on consumer search, click, and con-version behavior in the presence of organic listings ofthe same firm for the same set of keywords at the sametime. We aim to make the following four contributions:First, we build an integrative simultaneous equa-
tion-based model to empirically estimate the impactof ad rank and other keyword-level attributes onconsumer aggregate responses, and advertiser andsearch engine decisions in the presence of both paidand organic search listings. Specifically, we exam-ine the relationship of these attributes with averagesearch, click-through, and purchase propensities aswell as with the advertiser’s cost per click (CPC) andthe search engine’s decision with respect to allocat-ing keyword ranks in accordance with institutionalpractices. We find that on average the presence ofretailer-specific information and brand-specific infor-mation is a significant predictor of conversion rates
in paid and organic listings, respectively. A simul-taneous equations model as proposed in our studymakes it possible for us to describe current phenom-ena and prescribe some recommendations to adver-tisers. It also provides two key benefits. On one hand,we are able to account for the potential endogene-ity of keyword rank and CPC. On the other hand,this allows us to do some simple policy simulationsto infer the optimal CPC for different keywords andthereby impute the impact of sponsoring ads in thepresence of organic listings on firms’ profits.Second, we investigate the value to firms from par-
ticipating in such sponsored search advertising byexamining the nature of interdependence betweenorganic and paid listings using an aggregate keyword-level data set of clicks and conversions on paid andorganic links. We also explore the asymmetric natureof the relationship between these two forms of searchengine listings. Based on our model, we find that aver-age click-throughs on organic search listings have apositive interdependence with average click-throughson paid listings, and vice versa. This positive interde-pendence is also asymmetric such that the impact oforganic clicks on increase in utility from paid clicks forthe same firm is 3.5 times stronger than the impact ofpaid clicks on increases in utility from organic clicks.We provide details of alternative econometric modelsthat we build and estimate to explore this interdepen-dence. All models provide qualitatively similar results.Third, we conduct some counterfactual experiments
using policy simulations to highlight the magnitudeof the positive interdependence between these twoforms of advertising. We find that on an average,this positive interdependence leads to an increase inexpected profits for the firm ranging from 4.2% to6.15% when compared to profits in the absence ofeither of these. Furthermore, the positive interdepen-dence is the strongest in the case of the “least compet-itive” keywords (such as retailer-specific keywords)and weakest in the case of the “most competitive”keywords (such as brand-specific and generic key-words). Therefore, the proposed parsimonious mod-eling framework can help advertisers make optimaldecisions and investigate the value from participatingin such sponsored search advertising in the presenceof natural or organic listings in search engines.Finally, we describe a simple field experiment that
sheds further light on the predictions from our empir-ical model and analysis. It shows that given a set ofkeywords, combined click-through rates, conversionrates, and total revenues accruing to the firm in thepresence of both paid and organic listings is higherthan those in the absence of paid search advertise-ments. We find that although the presence of paidsearch advertisements takes some traffic away fromorganic listings for some keywords, for a vast majority
of keywords in our sample, the average click-throughrate of organic listings when paid search was on washigher than the average click-through rate of organiclistings when paid search was inactive. This resultshows that the positive interdependence effect pre-dicted by the econometric model is also corroboratedin controlled experiments and potentially suggests acausal interpretation to the results obtained from themodel.To evaluate the consistency of results between the
field experiment and the estimated model, we conductanalysis using the specific sample of keywords for theduration for which the experiment was run with paidlinks. The results from these analyses are consistentwith those from the integrated model and show thaton an average, paid click-through rates are positivelyassociated with organic click-through rates, and viceversa. Furthermore, the positive interdependence isalso asymmetric in nature. These results remain qual-itatively the same even when we estimate additionalmodel specifications such as the autologistic modeland the simultaneous-move game structural model.The remainder of this paper is organized as follows.
Section 2 gives an overview of the different streamsof literature related to our paper. Section 3 presentsa simultaneous model of consumer search, click, andpurchase; the advertiser’s keyword pricing decision;and the search engine’s decision of assigning key-word ranks. Section 4 presents an empirical applica-tion of the proposed model along with a descriptionof the data that are used. We also present a discus-sion of a number of robustness checks we have con-ducted using alternative model specifications such asan autologistic model and a simultaneous-move gamemodel. The details are in the electronic companion tothis paper, available as part of the online version thatcan be found at http://mktsci.pubs.informs.org. Wedescribe the counterfactual experiments conductedthrough some simple policy simulations in §5. Sec-tion 6 presents a controlled field experiment that alsoanalyzes the effect of organic search listings on paidsearch performance. Section 7 presents some manage-rial implications and concludes the paper with a dis-cussion of some limitations.
2. Literature and TheoreticalFoundation
Our paper is related to several streams of research.First, it relates to recent research in online advertising.A number of approaches have modeled the effectsof advertising based on aggregate data (Tellis 2004).However, much of the existing academic research(e.g., Gallagher et al. 2001, Drèze and Hussherr2003) on advertising in the online world has focusedon measuring changes in brand awareness, brand
attitudes, and purchase intentions as a function ofexposure. Other studies measure (individual) expo-sure to advertising via aggregate advertising dollars(e.g., Mela et al. 1998, Ilfeld and Winer 2002). Becausebanner ads have been perceived by many consumersas being annoying, traditionally they have had anegative connotation associated with it. Moreover, itwas argued that because there is considerable evi-dence that only a small proportion of visits translateinto final purchase (Moe and Fader 2003, Chatterjeeet al. 2003), click-through rates may be too imprecisefor measuring the effectiveness of banners served tothe mass market. Interestingly, however, Manchandaet al. (2006) found that banner advertising actuallyincreases purchasing behavior, in contrast to con-ventional wisdom. These studies therefore highlightthe importance of investigating the impact of otherkinds of online advertising such as search keywordadvertising on actual purchase behavior, because thesuccess of keyword advertising is also based on con-sumer click-through rates. Our study is also related toother forms of paid placements available to retailerson the Internet such as sponsored listings on shop-ping bots. For example, Baye and Morgan (2001),Montgomery et al. (2004), and Baye et al. (2009) havestudied the role of shopping bots as information gate-keepers and estimated the impact of retailers’ rankduring placement on click-through rates.From a theoretical perspective, our paper has inter-
esting parallels to the traditional product placementbased advertising next to editorial content in the massmedia. Shapiro et al. (1997) report a study of maga-zine advertising in which participants were requiredto read a magazine article delivered on a computerscreen. The article was flanked by target ads designedto receive minimal reader attention. They found thatusers were more likely to include the product fea-tured in the ad in their consideration set compared tothe control participants who had not viewed the ads.Geerardyn and Fauconnier (2000) discuss the adventof “advertorials,” which are printed advertising mes-sages but have the look and content of an ordinarynewspaper or magazine article. In creating the ad,the editorial form of the medium and article contentnext to which the ad is to be placed is taken intoaccount. Research in consumer behavior has theorizedabout these effects. For example, the truth effect (theincreased belief in an ad claim because of a previ-ous exposure; see Hawkins and Hoch 1992, Law andBraun 2000) and the mere exposure effect (the for-mulation of a positive affect from exposure to a briefstimulus; see Janiszewski 1993) both illustrate changesin consumer behavior following a single exposure toa stimuli without awareness of the prior exposure.There is also an emerging theoretical stream of lit-
erature exemplified by Edelman et al. (2007), Feng
et al. (2007), Varian (2007), and Liu et al. (2010) thatstudy mechanism design in sponsored keyword auc-tions. Athey and Ellison (2008) build a model thatintegrates consumer behavior with advertiser deci-sions. Wilbur and Zhu (2008) examine the incentivesof search engines to prevent click fraud. Katona andSarvary (2010) build a model of competition in spon-sored search and find that the interaction betweensearch listings and paid links determines equilibriumbidding behavior. Xu et al. (2009) find that whereasorganic listing may hurt search engine revenue, itcould induce higher social welfare and sales diversity.Despite the emerging theory work, very little empir-ical work exists in online sponsored search advertis-ing. Existing work has so far focused on search engineperformance (Bradlow and Schmittlein 2000, Telanget al. 2004) and examined issues related to adverseselection (Animesh et al. 2010) and pricing differencesbased on ad context (Goldfarb and Tucker 2007).Our paper is closely related to an emerging stream
of work that uses firm-level data from search engineadvertisers. Rutz and Bucklin (2007) study conver-sion probability for hotel marketing keywords in LosAngeles. Rutz and Bucklin (2008) also show that thereare spillovers between search advertising on brandedand generic keywords; some customers may startwith a generic search to gather information, but theylater use a branded search to complete their trans-action. Ghose and Yang (2008a) compare paid searchadvertising to organic listings with respect to predict-ing order values and profits. Ghose and Yang (2009)also quantify the impact of keyword attributes onconsumer search and purchase behavior as well ason advertiser’s cost per click and the search engine’sranking decision for different ads. They find that key-word rank influences not only ad click-through ratesbut also the final conversion rates from the adver-tiser’s website, thus implying that the value per clickis not uniform across slots on the search engine’sresults page. They also show that keywords that havemore prominent positions on the search engine resultspage, and thus experience higher click-through orconversion rates, are not necessarily the most prof-itable ones—profits are often higher at the middlepositions than at the top or the bottom ones. Agarwalet al. (2008) provide quantitative insights into theprofitability of advertisements associated with differ-ences in keyword position. Ghose and Yang (2008b)build a model to map consumers’ search–purchaserelationship in sponsored search advertising. Theyprovide evidence of horizontal spillover effects fromsearch advertising resulting in purchases across otherproduct categories. Yao and Mela (2009) build adynamic structural model to explore how the inter-action of consumers, search engines, and advertisersaffects consumer welfare and firm profits. Gerstmeier
et al. (2009) discuss some interesting bidding heuris-tics and highlight which of these leads to higher prof-its for the advertiser. Jerath et al. (2009) find that asuperior firm may obtain a position below the infe-rior firm but still obtain more clicks than the inferiorfirm. Thus, a firm may not always want to be in thetopmost position, a finding consistent with the rank-profitability relationship in Ghose and Yang (2009).
3. An Integrative Model of ConsumerResponse and Firms’ Decisions
We next present a model that integrates consumersearch and purchase behavior with firms’ decision-making behavior such as price of a keyword and therank of a keyword ad after the auction. This modelconsiders the simultaneous presence of both paid andorganic search listings. A hierarchical Bayesian mod-eling framework is used and the models are estimatedusing Markov chain Monte Carlo (MCMC) methods(Rossi and Allenby 2003).Let us denote Nit as the total number of searches
for keyword i in week t. We model the total num-ber of searches over time as a log-normal regressionspecified as follows:3
ln�Nit�= �i + �1Retaileri + �2 Brandi
+ �3 Lengthi + �4 Timeit +�it (1a)
�i ∼N� ��2�� (1b)
The covariates, Brand, Retailer, and Length, in theabove equation are described below. Prior work(Broder 2002) has analyzed the goals for users’ Websearches and classified user queries in search enginesinto three categories of searches: navigational (forexample, a search query consisting of a specific firmor retailer), transactional (for example, a search queryconsisting of a specific product), or informational (forexample, a search query consisting of longer words).Search engines not only sell nonbranded or generickeywords as advertisements but also well-knownproduct or manufacturer brand names, as well as key-words indicating the specific advertiser in order forthe firm to attract consumers to its website.4 More-over, advertisers also have the option of making thekeyword generic or specific by altering the number
3 We use a log-normal regression on the total search volumebecause of the existence of outliers, which do not make the normaldistribution a good one to apply.4 For example, a consumer seeking to purchase a digital camera isas likely to search for a popular manufacturer brand name such asNikon, Canon, or Kodak on a search engine as searching for thegeneric phrase “digital camera.” Similarly, the same consumer mayalso search for a retailer such as Best Buy or Circuit City to buy thedigital camera directly from the retailer.
of words contained in the keyword. Hence, we focuson the three important keyword-specific characteris-tics for a firm (the advertiser) when it advertises on asearch engine. This includes whether the keyword has(i) retailer-specific information (for example, “Wal-Mart,” “walmart.com”) or not, (ii) brand-specificinformation (for example, “Sealy mattress”) or not,and (iii) the length (in words) of the keyword(which determines how narrow or broad the con-sumer search is). Based on these factors, we con-struct three keyword-specific characteristics denotedby Brand, Retailer, and Length. The first two variablesare coded as dummy variables. The industry dynamiceffects are controlled for by adding a time trend in allequations.5 This is consistent with prior work in thisarea (see, for example, Ghose and Yang 2009).For a given keyword, although some searches do
not lead to any clicks at all, some searches lead toclicks on either organic or paid listings, and somesearches lead to clicks on both listings. This dual-click search behavior is also shown by Jansen et al.(2007), and hence it is important to incorporate suchdual-click search behavior in the model and analy-sis. Let N 10
it denote the number of click-throughs onthe same keyword only in the organic listing, let N 01
it
denote the number of click-throughs on the same key-word only in the paid listing, and let N 11
it denotethe number of click-throughs on the same keywordin both the organic and paid listings. The remainingN 00it = Nit − N 10
it − N 01it − N 11
it searches lead to zeroclick-throughs. Based on this, the likelihood functionis multinomial:
f �N 10it N 01
it N 11it N 00
it �
∝ �p10it �N10it �p01it �N
01it �p11it �N
11it �p00it �N
00it (2)
Let us further assume the probability of a click-through takes the logit form exp��it1�/�1+ exp��it1��for organic listings, and exp��it2�/�1 + exp��it2�� forpaid listings. Here, �it1 denotes the latent utility ofan average click on organic listings, and �it2 denotesthe latent utility of an average click on paid listings.Then by assuming the conditional independence of aclick-through on organic listings and a click-throughon paid listings, we can write down the four proba-bilities specified in Equation (2) as follows:
p10it =∫�it2
∫�it1
exp��it1�
1+ exp��it1�
· 11+ exp��it2�
p��it1�it2� d�it1 d�it2 (3a)
5 In addition to adding a time trend, we have also explored thespecification of correlated error terms over time. However, theautoregressive coefficients did not come out significant for any ofthe seven equations. Therefore, we present the results with timetrend effect.
We further model the interdependent relationshipof the two latent utilities associated with the twotypes of click-throughs for the same keyword asfollows:
�it1 = �it1 + �12i �it2 +�it1 (4a)
�it2 = �it2 + �21i �it1 +�it2 (4b)
The above two equations incorporate the notionthat the latent utility of an organic search and a paidsearch is dependent on both its intrinsic utility (�it)and the extrinsic utility from each other (�12i �it2 and�21i �it1). With respect to the intrinsic utility, we modelit to be dependent on the kind of keyword that isdisplayed in response to a search query. This is mod-eled as
With respect to the extrinsic utility, �12i and �21i indi-cate the effect that maps the interdependence betweenpaid listings and organic listings for keyword i. A pos-itive sign on �12i and �21i suggest a positive interde-pendency or complementary relationship between theclick-throughs via organic and paid listings. That is,the click-through on the organic (paid) listing tendsto increase the utility of a click-through on the paid(organic) listing. Similarly, a negative sign on �12iand �21i suggests a negative interdependency or sub-stitutive relationship between the click-throughs viaorganic and paid listings. Finally, a zero value of�12i and �21i suggests independence between the click-through via the organic and paid listings. Finally,we model the unobserved heterogeneity across key-words as
��i11�i12 �12i �
′ ∼MVN��1���1 � (6a)
��i21�i22 �21i �
′ ∼MVN��2���2 � (6b)
So far, we have modeled the click-through rates.Next, we model the conversion behavior conditionalon the click-through. Denote M1
it as the total num-ber of conversions for keyword i in week t fromorganic searches, M2
it as the total number of conver-sions for keyword i in week t from paid searches,and qit1 �qit2� as the conversion probability for organic(paid) searches conditional on a click-through. Thenassuming the conversions are independent events, wecan write down the likelihood of M1
it and M2it as
follows:
f �M1it �N 10
it N 01it N 11
it N 00it �
= �qit1�M1
it �1− qit1�N 10it +N 11
it −M1it (7a)
f �M2it �N 10
it N 01it N 11
it N 00it �
= �qit2�M2
it �1− qit2�N 01it +N 11
it −M2it (7b)
Prior work (Brooks 2005) has shown that there isan intrinsic trust value associated with the rank of alisting on a search engine, which leads to the conver-sion rate dropping significantly with an increase inthe rank (i.e., with a lower position on the screen).Another factor that can influence conversion rates isthe quality of the landing page of the advertiser’swebsite. Anecdotal evidence suggests that if onlineconsumers use a search engine to direct them to aproduct but do not see it addressed adequately onthe landing page, they are likely to abandon that site.Different keywords lead to different kinds of landingpages. In keeping with the institutional practices ofsearch engines, we use the click-through rates (CTRs)(standardized in our empirical analysis) to control forthe landing page quality score,6 where click-throughrate is defined as the number of clicks over the num-ber of searches. Furthermore, different keywords areassociated with different products. It is possible thatsome product-specific characteristics influence con-sumer conversion rates, and thus, it is important tocontrol for the unobserved product characteristics thatmay influence conversion rates once the consumer ison the website of the advertiser. Hence, we includethe three keyword characteristics to proxy for theunobserved keyword heterogeneity stemming fromthe different products sold by the advertiser. Thesefactors lead us to model the conversion probabilities
6 Google computes a quality score for each keyword as a functionof the relevancy, transparency, and navigability of information onthe landing page and the past click-through rate of that keyword(Ghose and Yang 2009). The key idea is to provide a higher userexperience after a click-through to the advertiser’s site from theirsearch engine. However, because we do not have information onthe landing page quality scores, we use the click-through rate asthe proxy for landing page quality scores. Further information onthis metric is available at http://www.adwords.google.com.
on organic listings �s = 1� and on paid listings �s = 2�as follows:
qits=(exp�cis1+cis2Rankits+�s1CTRits+�s2Retaileri
+�s3Brandi+�s4Lengthi+�s5Timeit+�its�)
·(1+exp�cis1+cis2Rankits+�s1CTRits+�s2Retaileri
+�s3Brandi+�s4Lengthi+�s5Timeit+�its�)−1
(8a)
�cis1cis2�′ ∼MVN�cs�
cs � (8b)
Next, we model the cost per click (CPC) ofthe ad keywords posted in the sponsored searchlist.7 Because different keyword attributes determinewhether it is a generic or branded keyword, theadvertiser’s CPC for a given keyword will dependon these attributes. The advertiser decides on its bidprice by tracking the performance of a keyword overtime such that the current bid price is dependent onpast performance of that keyword. It does this intwo ways.8 First, the keyword’s current bid price isa function of the rank of the same keyword in theprevious period, in both the paid and organic listing.Second, the keyword’s bid price is also based on theextent of profits from conversions through paid andorganic listings, respectively, in the previous period.Here, profit is defined as the revenue from adver-tising net of the variable cost of the product beingsold through that keyword minus the costs of plac-ing that advertisement for the firm (the advertisementcost is equal to the total number of clicks times costper click). Hence, we include both these sets of covari-ates.9 Finally, we also control for possible competitiveeffects of other advertisers by including the maximumbid price for a given keyword (denoted by Competitor_Price). This leads to the following equation:
7 Because we do not have data on actual bids, we use the actualcost per click as a proxy for the bid price. These two are highlycorrelated.8 This information about current bid prices being based on the twometrics of past performance (lagged profit and lagged rank) wasgiven to us by the advertiser. Our results are robust to the useof either one of these two metrics as well as to their exclusion.Gerstmeier et al. (2009) also discuss that current period bid can bea function of past profits from that keyword.9 Our results are robust to the use of gross profits in which we con-sider only the advertisement revenues and advertisement-relatedcosts as well net profits in which we consider the variable costs ofthe products.
Finally, we model the search engine’s decision onassigning ranks for the sponsored keyword. Searchengines like Google, MSN, and Yahoo! decide on theranks during the keyword auction by taking intoaccount both the current bid price and the qualityscore. Because the quality score is most affected bythe prior click-through rates, and more recent CTRis given higher weightage by the search engine incomputing this score, we use the one period laggedvalue of CTR (standardized in our empirical analy-sis) as a control variable. As before, we use the threekeyword attributes to proxy for the different unob-served characteristics of the landing page. We controlfor possible competitive effects of other advertisersby including the max bid price for a given keyword,Competitor_Price. This leads to the following equationfor the rank of a keyword in sponsored search:10
ln�Rankit2� = &i + '1 ln�CPCit�+ '2CTRi t−12
+ '3Retaileri + '4 Brandi
+ '5 Lengthi + '6Competitor_Pricei
+ '7 Timeit + vit (10a)&i ∼N�&2
&� (10b)
We allow the error terms in the five levels of deci-sions to be correlated. That is,
��it�it1�it2�it1�it2 %it )it�′ ∼MVN�0*� (11)
3.1. Econometric Issues and IdentificationThe specification of the covariance of the error termsis important to help control the potential endogene-ity in the keyword ranks for paid searches andconversions. To show this endogeneity issue and theidentification of the proposed system of simultaneousequation model, we provide a sketch of the modelbelow. The proposed seven equations, in essence, canbe written as follows:
Rank2 = f1�CPCX1,1� (12a)
CPC= f2�X2,2� (12b)
q1 = f3�Rank1X3,3� (12c)
q2 = f4�Rank2X4,4� (12d)
�1 = f5�Rank1X5,5� (12e)
�2 = f6�Rank2X6,6� (12f)
N = f7�X7,7� (12g)
10 There are three reasons for using the log (rank). First, rank is mea-sured as weekly average rank for a keyword, and therefore it is acontinuous variable rather than an integer. Second, the log transfor-mation makes its distribution closely mimic a normal distribution,and this mitigates the effect of outliers. Third, we have also triedan alternative linear model and found that the log-transformedmodel performs slightly better than the linear model for both thein-sample fit and out-sample fit.
In the above simultaneous equations system, X1–X7are the exogenous covariates associated with theseven equations, respectively. Note that X5 includesone covariate that is the instrument of �2, that is,��2. Similarly, X6 includes one covariate that is theinstrument of �1; that is, ��1. The terms ,1 ,7are the error terms associated with the seven equa-tions, respectively. These error terms are mainly cap-turing information that is observed by the decisionmakers (consumer, advertiser, and search engine) butnot observed by the researcher. The proposed sys-tem of simultaneous equations presented in Equa-tions (12a), (12b), (12d), and (12f) closely resemblesthe triangular system in standard econometric text-books (Greene 1999, p. 679). This model is identi-fied based on the following argument. First, Equation(12b) is a classical regression model whose parameterscan be naturally identified. To see this more clearly,CPC is modeled as exogenously determined (mod-eled as the advertiser’s decision and a function of theadvertiser’s past performance with the same keywordin both paid and organic listings, and other keywordrelated characteristics as specified in Equation (12b)).CPC, in turn, affects the search engine’s ranking deci-sion for paid ads, Rank2, and finally Rank2 affectsboth click-through and the conversion probabilities.Thus, Equations (12b)–(12g) can be identified accord-ingly. In fact, if the correlation between ,1 and eachof ,2 ,7 is equal to zero, then we can estimatethe seven equations separately. Now, if the correla-tion between ,1 and any of ,2 ,7 is not equal tozero, then Rank2 will be endogenous, and estimatingthese equations separately will lead to inconsistentestimates. We give a simple example in the follow-ing. Suppose that ,1 and ,2 have a nonzero correla-tion. Then in Equation (12b), Rank2 will be correlatedwith ,6 because Rank2 is correlated with ,1 and ,1 iscorrelated with ,6. The way to account for this endo-geneity problem is to simultaneously estimate Equa-tions (12a)–(12g). Because we are not able to predictthe correlation structure in the proposed simultaneousequations model, i.e., do not know which correlationis zero and which correlation is not zero, we estimatethe full covariance matrix and let the data inform us.As shown in Lahiri and Schmidt (1978) and dis-
cussed in Greene (1999), a triangular system ofsimultaneous equations can be identified withoutidentification constraints such as nonlinearity or cor-relation restriction. In particular, the identification ofsuch a triangular system comes from the likelihoodfunction. This is also noted by Hausman (1975), whoobserves that in a triangular system, the Jacobianterm in the likelihood function vanishes so that thelikelihood function is the same as for the usualseemingly unrelated regressions problem (Hausman1975). Hence, a GLS (generalized least squares)- or
SUR (seemingly unrelated regression)-based estima-tion leads to uniquely identified estimates in a trian-gular system with a full covariance on error terms asshown by Lahiri and Schmidt (1978).Furthermore, we did a simulation analysis and
found that our estimation procedure accurately recov-ers the true parameter values. This suggests that iden-tification is not a problem.
4. An Empirical ApplicationIn this section, we present an empirical application ofthe proposed model using a unique panel data set ofaggregate keyword-level data on clicks and conver-sions collected from a Fortune 500 firm that adver-tises on Google. We first describe the data-generatingprocess and the data used in the estimation, thendiscuss our empirical findings, and finally conductpolicy simulations based on the proposed model andparameter estimates.
4.1. DataWhen an Internet user enters a search query intoa search engine, he gets back a page with resultscontaining both the organic links most relevant tothe query and the sponsored links, i.e., paid adver-tisements that are ranked sequentially by the searchengine. The serving of a text ad in response to a queryfor a certain keyword is denoted as an impression. Ifthe consumer clicks on the ad, he is led to the land-ing page of the advertiser’s website. This is recordedas a click, and advertisers pay the search engine ona per-click basis. This is known as the cost per click.In the event that the consumer ends up purchasinga product from the advertiser, this is recorded as aconversion.Our data contain weekly information on paid
search advertising from a large nationwide retailchain that advertises on Google and is similar to thedata used in Ghose and Yang (2009).11 The data spanall keyword advertisements by the company duringa period of three months in the first quarter of 2007,specifically for the 13 calendar weeks from January 1to March 31. The data are based on an “exact match”between the user query and sponsored ad. Note thatsearch engines only provide aggregate-level daily orweekly data to advertisers. The use of exact match(instead of “broad” or “phrase” match) prevents anyconcern from possible aggregation biases arising as aresult of the absence of data from every single auctionthat occurred in a given week or in a given day. More-over, the firm providing us the data for this study
11 The firm is a Fortune 500 firm with a strong national and inter-national presence, but because of the nature of the data-sharingagreement between the firm and us, we are unable to reveal thename of the firm.
had confirmed that for an overwhelming majority ofthe keywords in our sample, there was very littlevariation in the number of competitors for a givenkeyword across the time period of our data. This fea-ture also minimizes the impact of competition on theextent of variation in the rank for a given keyword,further alleviating any concern of biases from dataaggregation.The data consist of keyword ads from all six cate-
gories of products that this nationwide chain retailersells (bedding, bath, dining, kitchen, electronics, andhome décor). These keyword ads encompass all the40 departments subsumed within these six productcategories. Between them, the keywords representseveral hundred unique stock-keeping units. We have106 unique brands represented by these keywords,and for the same advertiser we have several differ-ent combinations of its name, each represented by aunique keyword.Each keyword in our data has a unique advertise-
ment ID. For any given keyword search query, theretailer is linked through to both organic and paidsearch results on the search engine. In a given searchsession, whereas the majority lead to clicks on eitherorganic or paid (or no clicks at all), some searcheslead to clicks on both organic and paid listings dur-ing the same search session. We obtained the data onthe total number of searches for a given keyword in agiven week from the Google Keyword Metrics Tool.12
The data provided had information on the numberof clicks on “paid listings only,” number of clicks on“organic listings only,” and number of clicks on “bothorganic and paid listings” for any given keyword ona daily basis that was aggregated by the advertiser toa weekly basis. The number of searches that do notlead to any clicks is calculated by subtracting the sumof the aforementioned three types of clicks from thetotal number of searches. Similar to data on conver-sions through paid search, we have data on conver-sions through organic listings for any given keywordin the same week. Note that these are all aggregatekeyword-level data, not disaggregate user-level data.Data on organic search rankings for the same set of
keywords were obtained based on a Web crawler thatgathered information on where the advertiser’s linkwould appear on Google’s organic listings. The Web
12 This tool is available at http://www.technobloggie.com/keyword-tool/index.php and retrieves both daily and monthly searches fora given keyword on Google. We computed the weekly numberbased on the daily data. As a robustness check, we also computedthe weekly numbers based on the monthly data and find that ityields similar results. We used the total number of searches tocompute the click-through rates because we do not have data onthe total number of impressions on natural listings for a givenkeyword.
crawler was constructed in PERL. To get a more pre-cise estimate of the rank of the organic listing of theadvertiser, we retrieved these data once every weekover a six-week period from Google.13 Because therewas very little change in the rank of the organic list-ing (the standard deviation across ranks for a givenkeyword was very low), we used the weekly averagerank of a keyword in the organic listing for the pur-pose of our analysis. Finally, to control for competitivebid prices in our estimations, we collected data fromGoogle’s Keyword Pricing Tool, which gives estimatesof advertisers’ maximum cost per click for any givenkeyword. Google’s keyword estimator tools give twokey pieces of information: the estimated upper rangeand lower range for the cost per click of that key-word (roughly corresponding to the price of appear-ing ranked first and third on the sponsored linksrelated to that keyword). We take the average of thesetwo values to construct the Competitor_Price variable.Then for both paid and organic listings, we have
information on the number of clicks, number of con-versions, the total revenues from a conversion for agiven keyword for a given week, the average CPCin paid search, the maximum CPC for a given key-word across competitors, and the rank of the key-word. Although a search can lead to an impression,and often to a click, it may not lead to an actual pur-chase (which we define as a conversion). The prod-uct of CPC and number of clicks gives the total coststo the firm for sponsoring a particular advertisement.We have data on the contribution margin of each key-word based on the subproduct category (department)that it represents. Based on the contribution mar-gin and the revenues from each conversion througha paid search advertisement, we compute the grossprofit per keyword from a paid search conversion.The difference between gross profits and keywordadvertising costs (the number of clicks times the costper click) gives the net profits accruing to the retailerfrom a sponsored keyword conversion. This gives usthe Paid_Profit variable. Similarly, the Organic_Profitvariable is computed based on the contribution mar-gin of the keyword and the revenues from each con-version through an organic search listing.14
Our sample only includes those keywords forwhich we had access to data on total weekly searchesfor those keywords on Google. This resulted in a dataset with 426 unique keywords and a total of 1,400
13 The Web crawler performed searches with the exact keyword thatwe have in our data to search for the page number and rank of theorganic link of the advertiser that is retrieved by the search engine.14 The CPC for clicks on organic listing is always zero. We also ranall the estimations without factoring in the contribution margin ofthe different keyword. All our results are robust to the use of grossmargins only.
observations. Table 1 reports the summary statistics.Not surprisingly, a majority of the keywords havebrand-specific information (65%), whereas only 18.8%of the keywords have retailer-specific information.Interestingly, we note that the mean click-throughrate was 6.6% and 2.77%, respectively, from paidand organic searches. The mean conversion rate was5.71% and 1.67%, respectively, from paid and organicsearches. Finally, note that the mean profit from paidsearch advertisements was 3.1 times higher than thatfrom organic search listings.
4.2. Empirical FindingsFirst note from Table 2 that all three keyword-specific characteristics (Retailer, Brand, and Length)significantly predict the search volume. Specifically,retailer-specific keywords are associated with a highervolume of searches, whereas keywords containinginformation on brands (manufacturer or product)are associated with a lower volume of searches.Moreover, the volume of searches decreases with anincrease in the length of the keyword, i.e., an increasein the specificity of the search.From Tables 3(a) and 3(b) we see that the aver-
age magnitude of interdependence (the parameter �)between paid clicks and organic clicks is positiveand statistically very significant. Therefore, a higherprobability (number) of clicks on organic listings iscorrelated with a higher probability (number) of clicks
Table 2 Results on Search Volume
Response estimates Heterogeneity estimate
Intercept 5�74 3�71�0�12� �0�25�
Retailer 1�45�0�26�
Brand −0�23�0�10�
Length −0�55�0�00�
Time 0�001�0�002�
Note. Posterior means and posterior standard deviations (in theparentheses) are reported, and estimates that are significant at95% are in bold in Tables 2–6.
on paid search ads, and vice versa.15 This highlightsthat the presence of organic search listings has a pos-itive association with the average click-through ratesin paid search advertisements, and vice versa. Wealso find that the magnitude of this positive inter-dependence between paid search and organic searchis asymmetric. On average, the average impact of
15 The three characteristics of a keyword (Retailer, Brand, and Length)are all mean centered, and hence the intercept can be viewed as themean effect.
Table 3(a) Results on Paid Click-Throughs
Intercept Rank Retailer Brand Length Time Utility_Organic
organic clicks on increases in the utilities of a paidclick (0.98) is 3.5 times stronger than the averageimpact of paid clicks on increases in organic clicks(0.28). In addition, from Equations (3a)–(3d), we alsocomputed the individual probabilities p10it , p01it , andp11it and the lift in probabilities from a one unitincrease in utility based on the empirical estimatesand the summary statistics. We found that one unitincrease in paid utility increases organic click-throughprobability by 1.25 times more than vice versa.As predicted, Rank has an overall negative relation-
ship with CTR in both paid and organic listings asseen in Table 2. The position of the advertisementlink on the search engine results page clearly playsan important role in influencing click-through rates.This kind of primacy effect has also been seen inother empirical studies of the online world (Ansariand Mela 2003, Brynjolfsson et al. 2004, Rutz andBucklin 2007, Baye et al. 2009, Ghose and Yang 2009).Interestingly, the magnitude of the effect of rankon click-through rates is different for paid searchesfrom organic searches. The magnitude of the Rankcoefficient is smaller �−0 02� for paid searches thanfor organic searches �−0 06� suggesting that keywordposition on the screen plays a relatively more impor-tant role in influencing clicks in organic search com-pared to clicks in paid search.We find that neither the presence of a brand name
nor the retailer’s own name in the search keywordhas a statistically significant effect on click-throughrates in paid listings. However, in the case of organiclistings we find that the coefficient of Brand is pos-itive and significant (0.29), whereas that for Retaileris negative and significant �−0 58�. The coefficient ofLength is significantly positive in organic search (0.17),suggesting that longer keywords that typically rep-resent more goal-oriented searches for specific prod-ucts tend to experience higher click-through rates onorganic listings. As shown in Table 2, many of theestimated variances (unobserved heterogeneity) of theintercept, the interdependence effect, and the Rankcoefficient are significant in both organic and paidsearch click-through probabilities. This suggests thatthe baseline click-through rates and the way that key-word ranking predicts the click-through rates are dif-ferent across keywords, driven by factors beyond thethree observed keyword characteristics.Next, consider Tables 4(a) and 4(b) with findings
on conversion rates. We find that Rank has a negativerelationship with conversion rates from both paid andorganic searches but is statistically significant onlyfor organic listings. This implies that the lower theRank (i.e., higher the position of the sponsored list-ing on the screen), the higher is the Conversion Rate inorganic search. On the other hand, CTR has a posi-tive effect on the Conversion Rate in paid search but a
statistically insignificant effect in organic search con-version rates. Overall, this suggests that there is anindirect effect of Rank on the conversion probabilityfor paid search (through its effect on click-throughrate) but a direct effect for organic search. Our anal-ysis also reveals the coefficient of Retailer is posi-tive and significant for conversions in paid searchbut statistically insignificant for organic search. Asshown in Tables 4(a) and 4(b), many of the estimatedvariances (unobserved heterogeneity) for the inter-cept and the Rank coefficient are significant in bothorganic and paid search conversion rates. This sug-gests that the baseline conversion rates and the waythat keyword ranking predicts the conversion ratesare different across keywords, driven by unobservedfactors beyond the observed characteristics.The analysis of CPC in Table 5 reveals that Brand
has a statistically significant and negative effecton keyword cost per click. The coefficient of LagPaid_Rank is negative and statistically significantwhereas that for Lag Organic_Rank is negative butstatistically insignificant. Similarly, the coefficient ofLag Profit is statistically significant only in the caseof organic search listings. These findings suggest thatwhereas past performance metrics (lagged paid rankand lagged organic profit) are being incorporated bythe firm prior to bidding for keywords, it may not bebidding in an optimal manner. This is further evidentin the negative correlation of the Brand dummy withCPC. Given that brand-specific keywords are morecompetitive, one would expect this association to bethe other way around.
Table 5 Estimates of the Equation of ln(CPC) for Paid Searches
Response estimates Heterogeneity estimate
Intercept 0�162 0�047�0�009� �0�021�
Lag_Paid rank −0�071�0�022�
Lag_Organic rank −0�028�0�019�
Log(Lag_Paid profit) 0�002�0�002�
Log(Lag_Organic profit) −0�003�0�001�
Retailer 0�001�0�001�
Brand −0�017�0�003�
Length −0�004�0�006�
Competitor_Price 0�005�0�016�
Time −0�001�0�001�
On the analysis of keyword rank in Table 6, wefind that Brand and Retailer have a statistically signif-icant and negative relationship with Rank, suggestingthat keywords that have brand-specific information orretailer-specific information generally tend to be listedhigher up on the screen. Both CPC and Lag CTR arestatistically significant and inversely related to Rankas expected (see, for example, Ghose and Yang 2009).Furthermore, the effect of maximum bid price acrossall competing firms on Rank is also positive and statis-tically significant, thereby confirming that the extentof competition from other advertisers plays a key rolein the sponsored search auctions’ outcomes.Finally, it is worth noting in Table 7 that the unob-
served covariance between several variables is statis-tically significant. This suggests that keyword rankingis endogenous and a firm’s bids for a given keywordare likely to be based on the same keyword’s pastperformance.
To demonstrate the robustness of our main resultsusing the integrated model, we also explore two alter-native model specifications. In particular, we buildtwo nonnested models. First, we build and estimatean autologistic model to examine the sign of the inter-dependence between paid and organic click-throughs.Thereafter, we explore the nature of this interdepen-dence to examine if there is some kind of asymme-try in the relationship using a simultaneous-movegame structural model. For brevity, we only providea high-level description of the models below. Detailed
Table 6 Estimates of the Equation of Log(Rank) for Paid Searches
Response estimates Heterogeneity estimate
Intercept 1�51 0�84�0�06� �0�11�
CPC −4�19�0�27�
Lag_Paid click-through rate −0�18�0�05�
Retailer −1�01�0�15�
Brand −0�47�0�13�
Length −0�13�0�09�
Competitor_Price 0�33�0�08�
Time 0�07�0�01�
descriptions along with the estimates are given in theelectronic companion.
4.3.1. Autologistic Model. The autologistic modelthat is used to model the relationship between con-sumer click-throughs on paid and organic links hasbeen adopted in the marketing literature (for exam-ple, Moon and Russell 2008). The main idea behindthe autologistic model is to allow the click-throughaction to be interdependent on each other instead ofthe latent utility as in our main model. More specif-ically, the autologistic model starts with a specifica-tion on the conditional distribution of one event suchas a click-through on a paid or organic listing. Thenbased on the Besag’s (1974) theorem (also known asBrook’s lemma), this conditional specification leadsto a proper and well-defined joint distribution of theclick-through probabilities of paid and organic search,given that the interdependence effect is symmetric.The intrinsic utility functions for paid and organicclicks are a function of the different keyword-levelcovariates and other factors that determine potentialbenefits to the consumer from a click.We find that the average magnitude of interde-
pendence (the interdependence parameter �) betweenpaid clicks and organic clicks is significantly positive.Therefore, a higher probability (number) of clicks onorganic listings is correlated with a higher probability(number) of clicks on paid search ads, and vice versa.The results of the click-through estimates are given inTables A.1(a)–A.1(c) of the electronic companion.
4.3.2. Simultaneous-MoveGameStructuralModel.Given the positive interdependence we find betweenpaid and organic clicks in our data using the autol-ogistic specification, we further explore the presenceof an asymmetric effect in this relationship by adopt-ing a structural approach (Bresnahan and Reiss 1991).
As shown in Bresnahan and Reiss, we need to knowthe signs of the interaction effects �s to solve for theequilibrium in this structural modeling approach. Forexample, �s are assumed to be negative in a discreteentry game by assuming that competitors’ entry tendsto lower the company’s profit at entry; �s are assumedto be positive in studying social interactions or peereffects among consumers. As shown in Bresnahan andReiss, a violation of this assumption can lead to theabsence of an equilibrium. Given the positive inter-dependence we find between paid and organic clicksin our data using the autologistic specification, wecan explore the existence of an asymmetric interde-pendence by constraining the interaction effects to bepositive. We use the hierarchical Bayesian method toestimate this model. As before, we find evidence ofa strong asymmetric effect. On average, the effect oforganic search click-throughs on paid ad clicks is 3.1times the effect of paid ad click-throughs on organicsearch clicks. The results of the click-through esti-mates are given in Tables A.2(a)–A.2(c) of the elec-tronic companion.We have also run multivariate regressions with
panel data methods such as fixed effect models, ran-dom effect models, and Tobit regressions. Those anal-yses also show a strong positive interdependencebetween paid clicks and organic clicks and are thusvery consistent with our current model. The regres-sion model is specified in the appendix, and theresults are in Table A.3 of the electronic companion.16
16 We ran further robustness checks such as adding (i) a dummyvariable indicating if the organic listing was on the first page whenthe paid listing was on the first page and (ii) another specification ifthe organic listing of this advertiser appeared more than once in thefirst 10 pages of Google’s search engine results. We also ran addi-tional robustness tests such as whether the paid listing for a givenkeyword appeared on the first page of the search engine results
4.3.3. Both Interdependence and Independence.As a robustness check, we also explore an alterna-tive specification that incorporates both interdepen-dence (� �= 0� and independence (� = 0� in modelingthe paid and organic click-throughs. This is consistentwith modeling structural heterogeneity in the market-ing literature. In such a model the probability (likeli-hood) of one observation yk can be written as
Lk = pL1k�yk � � �= 0�+ �1− p�L2
k�yk � �= 0� (13)
In this mixture specification, p is the point mass orprobability of following the interdependence modeland 1 − p is the point mass or probability of fol-lowing the independence model. We estimate thismodel, using the Bayesian approach developed inYang and Allenby (2000) for dealing with the struc-tural heterogeneity. The qualitative nature of all ourestimates remains the same. More importantly, ourresults showed that there is a point mass of 0.972 onthe interdependence model (L1
k�yk � � �= 0��. This pro-vides strong evidence for confirming the validity ofour original model that incorporates the interdepen-dence specification only.4.3.4. Out-of-Sample Prediction. To demonstrate
the fit of our model, we conduct an out-of-sampleprediction. Based on the mean absolute deviations(MAD), our results suggest that the proposed simul-taneous equation model predicts better than the samemodel estimated equation by equation, suggestingthe importance of accounting for the simultaneity. Inaddition, we find that our proposed model predictssubstantially better than a naïve non-model-basedforecasting approach (i.e., predicting with sampleaverage), which emphasizes the need for a model.
page when the organic listing was on the first page. The qualitativenature of our main result of positive and asymmetric interdepen-dence between the two forms of listings remains the same in allthese analyses.
We aim to assess how much the advertiser bene-fits from the simultaneous presence of both paid andorganic search listings. To this end, we first need toinfer what the maximum profits for the advertiserare from both paid and organic search, which in turnrequires that we infer the optimal cost per click foreach keyword based on the empirical estimates from§4.2. The advertiser can determine the optimal CPCfor each keyword to maximize the expected profit �/�:
In Equation (17), pit is the expected CTR for key-word i at week t and the superscripts indicate click-through rates on organic, paid, or both, consistentwith Equation (2). qit is the expected conversion rateconditional on a click-through, and mit is the expectedgross profit from a conversion that is observed fromour data. Subscripts 1 and 2 in qit and mit indi-cate organic and paid search, respectively. CPCit isthe actual cost per click paid by the advertiser tothe search engine for a given keyword. pit , qit , andRankit are predicted based on Equations (3a)–(3c),(8a)–(8b), and (10a)–(10b), respectively, using the esti-mates obtained from the proposed model. Note thatthis kind of analysis cannot be done by eyeballing thesummary statistics of the data because it requires usto find the optimal profits of the advertiser based onimputing the optimal CPC.We conduct the optimization routine to maximize
the expected profit from each consumer impressionof the advertisement for each keyword in each week,using the grid search method. Our simulation resultshighlight that there is a considerable difference in theoptimal CPC and the actual CPC incurred by the firmfor a given keyword. Furthermore, there is also a dif-ference between optimal expected profits and actualprofits accruing to the firm from the current CPC.These results show that the firm was not biddingoptimally during the time period of our data. Forthe majority of the keywords, we saw evidence ofoverbidding by the firm. Note that a similar findingregarding the suboptimal bidding behavior was dis-cussed in Ghose and Yang (2009), who used a similardata set from the same firm.We conduct a counterfactual experiment to infer the
magnitude of the positive interdependence betweenorganic search and paid search, and vice versa. Tothis end, we run the policy simulation in the absenceof the cross-advertising effect ��� parameter. Thatis, we set the cross-advertising effect parameter tozero and then calculate the optimal CPC and theexpected profit, given the optimal CPC. We find thatthe expected profit in the presence of the � parameteris 4.25% higher than that in its absence.
To check for the robustness of these results, we alsodid a few simulations that are more specific. First,we reran the simulation using a sample consisting ofonly retailer-specific keywords. This is the set of key-words where we expect the advertiser to face the leastamount of competition because only the advertiser islikely to bid on such keyword ads that prominentlydisplay its name.17 Second, we reran the simulationusing a sample consisting of branded and generickeywords only. This is the set of keywords wherewe expect the advertiser to face the most competi-tion because all firms selling a similar portfolio ofproducts are likely to bid for such ads. Indeed, ourdata suggest that the CPC for branded and generickeywords was 2.1 times that of retailer-specific key-words. Furthermore, the CPC of generic keywordswas 1.2 times that of branded keywords.Our findings are consistent with the main result.
Using the “retailer-specific keywords” only, we findthat the expected profit in the presence of the inter-dependence effect parameter is 6.15% higher thanthat in its absence. Using the “generic and brandedkeywords,” we find that the expected profit in thepresence of the cross-advertising effect parameter is4.2% higher than that in its absence. Thus, the addi-tional implication we can derive from these exper-iments is that the positive interdependence is thestrongest in the case of the “least competitive” key-words (retailer-specific keywords) and weakest in thecase of the “most competitive” keywords (brand-specific and generic keywords).We also conducted simulations using different sub-
samples as robustness checks. Specifically, we lookedat different ways to consider the cases where the paidlink was not displayed on the first page in the eventthat this increase in profits was mostly for such links.Note that Google’s sponsored search auction has nofixed format for the number of links that appear onthe first page for any given search query. Anecdotalevidence suggests that the number of sponsored linkson the first page could vary anywhere between 3 and10 for a given keyword. Thus in our data we lookedat cases where the rank of the keyword in the paidsearch auction was (i) more than 3, (ii) more than 5,and (iii) more than 10, and we ran the policy sim-ulations separately on these subsamples. We foundthat even if the paid link did not appear on the firstpage, there was an increase in profits from the posi-tive interdependence between paid and organic rang-ing from 2.6% to 4.2%.
17 We verified this information from the Search Analytics tool ofhttp://www.compete.com and found that on an average the totalclick-through share of the retailer-specific keywords belonging tothis advertiser’s direct competitors is only 1.8%. In other words,almost all referrals to the advertiser’s website stemming fromretailer-specific keywords originate from the firm’s own sponsoredadvertisement.
6. A Field ExperimentOur empirical model and analysis in §4 predicts thatthe combined CTR from paid and organic search list-ings when both these options are available to users isgoing to be greater than or equal to the CTR from thescenario where there are only organic search listingsavailable. To put it in terms of the model parame-ters, recall from Equations (3a)–(3d) that the combinedCTR in the presence of the interdependence effectparameter � is given by p10it + p01it + p11it . This expres-sion is greater than or equal to p10it in the absence ofpaid search, depending on the magnitude of searchersbelonging to the p01it and p11it categories who shiftto clicking on organic search links. Furthermore, themodel predicts a positive interdependence betweenclicks on paid and organic listings. In this section,we describe a simple field experiment that was con-ducted to shed further light on these predictions fromthe empirical model.Let 1 be the fraction of users who move from click-
ing on paid search to natural links when the firmpauses sponsoring ads. Intuitively, this shift occursbecause users who would have clicked on paid linkswould only have the option of clicking on organiclinks when the firm does not engage in paid search.Based on the model it is not obvious if all users offirm’s paid search ads would migrate to click on itsorganic links (1= 1) or only a fraction of them woulddo so (1< 1). If it turned out that 1= 1, that wouldimply that the combined CTR was the same as theCTR when only organic listings are available, and onewould question the value to the firm from engag-ing in sponsored searches given the costs involved inpaid search advertising. Perhaps even more impor-tantly, if the total revenues in the presence of bothpaid and organic search listings are not significantlyhigher than the revenues when only organic searchlistings are present, the potential value from spon-sored searches would be rather murky.A second related question would be to analyze
how the click-through rate in organic listings specif-ically would change if the advertiser moved fromsponsoring paid searches to turning the ads off. Inother words, we are interested in comparing the click-through rate of organic searches in the “both organicand paid” scenario versus the “only organic” sce-nario to examine the effect of paid ads on the CTRof organic listings per se. Our model suggests thatthis would be a function of the respective CTR prob-abilities and the fraction of people who migrate fromclicking on paid ads to clicking on organic listings fora given keyword.To be precise, we derive this cutoff in the follow-
ing way. Recall from Equations (8a)–(8d) that in thepresence of a paid ad, the total probability of click-ing on organic listings is p10it + p11it . In the absence of
paid ads, the total probability of clicking on organiclistings is p10it + 1�p01it + p11it �. This implies that theorganic CTR will be higher or lower in the absence ofpaid search depending on a critical value of 1 givenby p11it /�p01it + p11it �. Whether this organic CTR wouldbe higher or lower is therefore an empirical question.To investigate these two issues, a field experiment
was designed that sheds further light on the impact ofthe simultaneous presence of paid search and organiclistings on the combined performance from thesetwo listings. This experiment was conducted over aneight-week period from mid-March to mid-May in2007 during which the firm pulsated between peri-odically sponsoring some keywords and then haltingthe process. Specifically, a sample of 90 keywords wasrandomly selected by the firm to conduct this exper-iment. Then the firm sponsored these keyword adsfor a two-week period on Google and tracked theresults from the organic and paid search advertise-ments. Then the firm paused the sponsored adver-tisements for the next two weeks and tracked onlythe results from the organic listings. Then it resumedsponsoring the same set of keywords again for thenext two weeks and then paused the process for theremaining two weeks. During these pulsing periods,the firm measured both sponsored search and organicperformance using different metrics such as click-through rates, conversion rates, and revenues.Based on the analysis of this field experimental
data, we found that when paid search advertising wasactive implying that both sponsored and organic list-ings were available to consumers, the combined CTRfrom both of these listings was 5.1% higher than whenpaid search advertising was inactive, and only theorganic listings were present (see Figure 1(a)). A twosample t-test reveals that the difference is statisticallysignificant at the 1% level. It is worth noting that fora vast majority of the keywords, we found that theCTR of organic listings in the both organic and paidscenario was higher than its CTR when paid searchwas inactive.After verifying that paid search keywords provide
additional visitors to the advertiser’s website, it wasimportant to monitor the quality of traffic driven bypaid search keywords. We find that although paidkeywords are running alongside the organic links, thecombined conversion rate is higher than when theorganic links stand alone on the search engine resultspage. When paid ads are active, the combined conver-sion rate from both paid and organic links was 1.53%.Thus, there is an 11.7% increase in the combined con-version rate when paid and organic links are presentsimultaneously relative to when only organic listingsare present (Figure 1(b)). Furthermore, when paid adsare paused, the conversion rate from organic search
Figure 1(a) Plot from the Field Experiment Showing Combined CTRfrom Paid and Organic Search in the Periods When PaidSearch Advertising Was On and When Paid SearchAdvertising Was Paused
Total CTR from paid and organic search
0.00
5.00
10.00
15.00(%)
20.00
25.00
30.00
Total CTR 25.20% 20.10%
1 2
Figure 1(b) Plot from the Field Experiment Showing CombinedConversions from Paid and Organic Search in the PeriodsWhen Paid Search Advertising Was On and When PaidSearch Advertising Was Paused
Total conversion rates from paid and organic search
1.25
1.30
1.35
1.40
1.45
(%)
1.50
1.55
Total conversion rates 1.53% 1.37%
1 2
Figure 1(c) Plot from the Field Experiment Showing CombinedRevenues from Paid and Organic Search in the PeriodsWhen Paid Search Advertising Was On and When PaidSearch Advertising Was Paused
was 1.37%. It is worth noting that, for a vast major-ity of the keywords, the conversion rate of organiclistings in the both organic and paid scenario washigher than its conversion rate when paid search wasinactive.With respect to revenues, we observed peaks and
valleys in performance as and when the paid adswere pulsed. Because the firm tracked revenues frompaid and organic searches separately, we were able toverify that although organic keywords made up a por-
tion of the lost revenue when paid search keywordswere inactive, organic listings alone did not providethe full value of having both paid and organic searchsimultaneously available to users. Through the anal-ysis of these data, we found that when paid searchadvertising is active, it drives an additional 54% incre-mental revenue lift from $435K to $682K in total rev-enue (Figure 1(c)). A t-test reveals that this differenceincrease is statistically significant. The substantiallyhigher increase in combined revenues compared tothe increase in combined click-through and conver-sion rates suggests that users tend to buy a greaternumber of products or buy higher-value items whenpaid search is active. This highlights the strong busi-ness potential of paid search.To further evaluate the consistency of results
between the field experiment and the estimatedmodel, we conduct some panel data analysis using thespecific sample of keywords for the duration for whichthe experiment was run with paid search advertise-ments on. We regress paid click-through rates againstorganic click-through rates after controlling for theRank of the keyword in paid search, and vice versa.In particular, we estimate ordinary least-squares (OLS)regressions with keyword-level fixed effects. We alsoestimate the same regressions with keyword-level ran-dom effects and find that the estimates are very similarin magnitude and direction. These regressions predictthat paid click-through has a statistically significantand positive relationship with organic click-through,and vice versa. In addition, the effect is also asym-metric. Based on the magnitude of the coefficients, wefind that the effect of organic click-through on paidclick-through is significantly higher than the effect ofpaid click-through on organic click-through. Note thatthis is consistent with our finding from the economet-ric model, including the alternate ones conducted forrobustness purposes.
7. Discussion, Implications, andLimitations
We build a model that integrates consumer searchesand their reactions to the organic listings and spon-sored ads associated with these searches with theadvertiser’s decision on cost per click and the searchengine’s decision on keyword ranks. Our goal is toestimate the interdependence between organic andpaid ads. The model is general and can be directlyapplied to many Internet firms who sell their prod-ucts on the Internet and advertise their products viasearch engines. Our data are also unique and care-fully screened to prevent any possible concerns fromthe use of aggregate-level data.18
18 As mentioned in §4, these features in the data include the use of“exact match” to display ads and the use of a sample with very
We show that the presence of organic listings isassociated with a higher probability of click-throughson paid ads, and vice versa. This suggests thatfirms, which tend to rank highly in organic search,are more likely to benefit from sponsored searchadvertising. In this regard, our finding that paidand organic listings have a positive interdependenceon each other’s click-through rates underscores thatboth search engine optimization (SEO) and searchengine marketing (SEM)—along with other market-ing channels—have a place in online customer acqui-sition campaigns. Thus, these results can have usefulimplications for a firm’s marketing mix strategies. Thisempirical finding is consistent with claims in the tradepress that more people will visit a website if it islisted in both paid and organic listings because thereis a “second opinion effect.” This happens becausesearchers are encouraged by the fact that a websiteis listed in both the organic and paid listings leadingto higher click-through rates.19 Another reason couldbe related to the quality of the link and the resul-tant consumer satisfaction from a click on each typeof link. This is possible because the landing pagesassociated with a keyword might be different fororganic and paid links, and the right landing page onthe organic listing could be strategically decided bythe search engine. In a game-theoretic model, Taylor(2009) shows that by adjusting the quality of organiclinks and thereby affecting the level of consumer sat-isfaction from clicking on a link, search engines caninduce consumers to click on both organic and paidlinks, leading to a positive interdependence betweenorganic and paid listings. White (2008) also exploresthe costs and benefits to a search engine of providingInternet users with high-quality organic search resultsin addition to showing them paid advertisements anddiscusses similar effects on user behavior.Furthermore, we find that the relationship is asym-
metric such that the impact of organic clicks on anincrease in utility from paid clicks is on an aver-age 3.5 times stronger than vice versa. From a searchengine’s perspective, this positive and asymmetricinterdependence between paid and organic listingsalso implies that the top-ranking websites in organicsearch are likely to get a higher number of clicks inpaid search as well. Because advertisers pay searchengines on a per-click basis, this has implicationsfor search engines’ revenues. Indeed, there may bea moral hazard problem here as search engines mayhave an incentive to manipulate rankings in organicsearch and selectively present those firms on the
little variation in the number of competitors for a given keyword.These features reduce the variation in ranks within a given day andthereby allow us to gain precise estimates using aggregate data.19 See Hartzer (2005).
top in organic search that experience higher click-through rates in paid search. Search engines claimthere is no direct linkage between sponsoring adsand organic ranking, but trade press reports specu-late that there could be perverse incentives for searchengines.20 Google creates algorithms that generateorganic search results based on indexing criteria suchas relevance, PageRank, and the presence of user-generated content (UGC). Even though sponsored adsdo not count towards the link popularity of an adver-tiser in the organic listings, there are other waysto tie together paid ads and organic listings. Forexample, Google has begun to serve organic searchresults based on user profiles in its recently devel-oped personalized search results. Websites that usershave already visited will usually rank higher on sub-sequent queries if users have that feature enabled.A potential implication is that a firm might pay tohave a paid listing for the most generic of termsbecause a click on a paid ad helps it rank higheron the organic listings in subsequent searches as theuser gets closer to the purchase. Thus, there could bedeleterious effects of interactions between paid andorganic listings. Another example of an intricate rela-tionship between paid and organic listings is throughUGC. Whereas Google ranks landing pages with UGChigher in its organic search, the presence of UGC canalso increase the landing page quality scores. Thishighlights the importance of having UGC on websitesfor improving rankings in both paid and organic list-ings. On the other hand, selective presentation of paidlinks or organic links could also improve consumerutility by reducing the cognitive costs associated withevaluating different alternatives. This has been shownby prior research on information gatekeepers likeshopbots (Montgomery et al. 2004) whose infrastruc-ture for paid placement of retailers (pay per click) isvery similar to that of search engines. This calls atten-tion for the need for designing newer mechanismsthat can preserve the integrity of organic search rank-ings while still increasing user welfare during search.In most search-based advertising services, a com-
pany sets a daily budget, selects a set of keywords,determines a bid price for each keyword, and des-ignates an ad associated with each selected key-word. With millions of available keywords and ahighly uncertain click-through rate associated with
20 Google’s official claim is that “it is very important to note thatthere is absolutely no connection between being an AdWordsadvertiser, and having your site appear in the unpaid search results.One does not affect the other in any way. To put it anotherway, being an AdWords advertiser will neither help nor harmyour chances of appearing on the ‘organic’ search engine” (SearchEngine Roundtable 2007). White (2008) also highlights that despitethe regulatory eyebrows Google has been raising, there is remark-able silence over the incentives to manipulate the organic listings.
the ad for each keyword, identifying the most prof-itable set of keywords given the daily budget con-straint often becomes challenging for firms wishingto promote their goods and services via search-basedadvertising (Rusmevichientong and Williamson 2006).The analysis of keyword covariates on average click-through rates and conversion rates can provide someguidance to practitioners on the profitability of choos-ing different keywords. Indeed, such techniques couldnicely follow the broader keyword selection tech-niques based on popularity and economic impactof occurrence of keywords in user-generated con-tent sites such as product review forums and blogs(Archak et al. 2007, Dhar and Ghose 2009).Our estimates also suggest that firms may not be
bidding optimally based on the relationship betweencost per click and different keyword attributes, consis-tent with the findings of Ghose and Yang (2009). Thiscan provide additional managerial implications forfirms engaging in paid search advertising. Based onan optimization algorithm that imputed the expectedprofits based on the optimal CPC for each keywordfor the advertiser, we find that as a result of thepositive interdependence, the firm’s profits in thesimultaneous presence of paid and organic searchlistings is 4.5% higher compared with the scenariowhen there are either only paid advertisements ororganic search listings. Furthermore, we find that thepositive interdependence is the strongest in the caseof the “least competitive” keywords (retailer-specifickeywords) and weakest in the case of the “mostcompetitive” keywords (brand-specific and generickeywords). Therefore, the proposed parsimoniousmodeling framework can help advertisers make bet-ter decisions about investments in sponsored searchin the presence of organic listings in search engines.Finally, we describe a field experiment that shows
that total revenues and combined conversion ratesin the presence of both paid and organic listings arehigher compared to when only organic listings arepresent. By examining the CTR, conversion rates, andtotal revenues, this experiment further corroboratesthe beneficial effect of the simultaneous presence oforganic and paid listings to advertisers. For manykeywords, the click-through rate in organic listings ishigher when paid and organic listings are simultane-ously available compared to when the firm does notsponsor keyword ads. Furthermore, the overall effecton combined click-through rates, conversion rates,and revenues is significantly positive. From a man-agerial standpoint, what makes matters a little moresubtle is that the conversion rates are higher on thepaid listings. This is true both in the empirical anal-yses as well as in the field experiment. It is possiblethat users are self-selecting: searchers who are morelikely to convert are more likely to click on the paid
listing. It is somewhat intuitive that people who areless likely to convert (information seekers, consumersearly in the purchase process, or those with othernoncommercial goals) are going to lean more towardclicking on organic listings rather than paid listings.This would naturally lead to a higher conversion ratevia paid ads. It is also possible that the sponsoredads are written better to grab more targeted trafficand send users to better landing pages than organiclistings.Our results have some implications on how adver-
tisers should invest in SEO, in which firms try toimprove their ranking in organic search by fine tun-ing their landing pages versus SEM, in which firmstry to improve their performance in paid search auc-tions. This can be important because many advertis-ers engage in both kinds of activity. Our data revealthat the conversion rate is significantly higher in paidsearch than in organic listings. This underscores theimportance of securing a higher rank and design-ing effective landing pages by advertisers. On theother hand, our analysis suggests that most of thekeyword-level characteristics have a stronger impacton the performance of organic search than paidsearch. For a well-rounded and effective search mar-keting campaign that reaches the greatest number ofsearchers, marketers should blend both organic andpaid listings, capitalizing on the positive interdepen-dence in clicks between them. These results couldshed light on understanding how firms should investin search engine advertising campaigns relative tosearch engine optimization and the proportion of theadvertisement budget allocated to search advertising.This paper has many important limitations that
suggest that these results might best be viewed asstarting points for further research. Some of thelimitations have to do with the lack of informationin our data. For example, we do not have data oncompetition—that is, we do not have information onthe competitors of the specific firm whose data wehave used in this paper. Hence, we are not able tocontrol for the impact of the number of ads displayedin response to a single search query while estimat-ing the relationship between paid and organic links.Although we use the maximum of the competitors’bid prices as the proxy for the level of competitionfor a given keyword, it is possible that we are over-estimating the extent of interdependence for highlycompetitive ads. That said, the firm providing us thedata for this study had confirmed that there was verylittle variation in the number of competitors for agiven keyword across the time period of our datafor the majority of the keywords. Nevertheless, futureresearch could use richer data sets to address thisissue.
We do not know whether the same consumerclicked multiple times on a given listing (for example,by using the browser’s back button to go back to thesearch engine results page from the advertiser’s page)or whether they clicked only once on each of theselistings within a given search session. Knowledge ofthis issue can motivate another empirical frameworkthat incorporates an incidence and count model todescribe this phenomenon.Another key limitation of our field experiment is
that we are unable to control the presence of organiclistings for a given keyword. It would be interestingto observe what happens to clicks and conversionson paid ads when organic search listings are absent,although such an experiment is only possible with theexplicit cooperation of the search engine or by care-fully designed laboratory experiments with humansubjects.An important avenue for future research is to
investigate the impact of consumer heterogeneity insearch advertising by adopting methods from recentmethodological advances in Bayesian modeling (Rossiand Allenby 2003, Chen and Yang 2007, Musalemet al. 2009). We did not model this because our pro-posed model based on aggregate data is already verycomplicated because of the simultaneous and nonre-cursive nature of the model. Future research could useindividual consumer-level data from multiple adver-tisers as opposed to one advertiser to model theimpact of consumer heterogeneity.Future research could also examine data on the tex-
tual content in the copy of the ad (ad creative) corre-sponding to the different keywords to examine howtextual content affects the results identified in thispaper. This can be done using recent advances in textmining methods for quantifying the economic impactof textual content (Archak et al. 2007), although someanecdotal evidence suggests that the presence of thekeyword in the title of the ad is more important thanthat in the ad copy in influencing clicks (Market-ing Experiments 2005). Notwithstanding these limita-tions, we hope that this study will generate furtherinterest in exploring this important emerging area inmarketing.
8. Electronic CompanionAn electronic companion to this paper is available aspart of the online version that can be found at http://mktsci.pubs.informs.org/.
AcknowledgmentsThe authors are listed in reverse-alphabetical order andcontributed equally. They are grateful to the associate edi-tor and two anonymous referees for extremely helpfulcomments. The authors also thank Susan Athey, MichaelBaye, Eric Bradlow, Erik Brynjolfsson, Mark Schankerman,
and seminar participants at Carnegie Mellon University,Columbia University, McGill University, Federal TradeCommission, New York University, Purdue University, Uni-versity of Calgary, University of Connecticut, University ofCalifornia at Irvine, University of Goethe Frankfurt, Univer-sity of Pennsylvania, University of Washington, MicrosoftResearch, the 2008 International Conference, the 2008 Mar-keting Science Institute conference, the 2008 NET InstituteConference, the 2008 International Symposium on Informa-tion Systems, the 2008 Workshop on Information Technol-ogy and Systems, the 2008 Workshop on Information Sys-tems Economics, and the 2009 Toulouse Conference on TheEconomics of the Internet and Software for useful sugges-tions. Anindya Ghose acknowledges the generous financialsupport from National Science Foundation CAREER AwardIIS-0643847. The usual disclaimer applies.
Appendix. The MCMC AlgorithmWe ran the MCMC chain for 40,000 iterations and usedthe last 20,000 iterations to compute the mean and stan-dard deviation of the posterior distribution of the modelparameters.
1. Draw �it = ��it1�it2�′.
As specified, the likelihood function of the number ofclicks is
l(N 10it N 01
it N 11it N 00
it
)∝ �p10it �N
10it �p01it �N
01it �p11it �N
11it �p00it �N
00it
The probabilities of the four actions (based on whether toclick on a paid listing, and whether to click on an organiclisting) conditional on the latent utilities �s, are as follows:
where ��it1 and ��it2 are predicted utilities from the reduced-form model on click throughs, generated in a separateMCMC chain in parallel to this algorithm. More specifi-cally, the reduced form of our click-through model can bewritten as
This approach follows the econometric literature for esti-mating similar models with endogenous regressors (Nelsonand Olsen 1978, Maddala 1983, Bajari et al. 2006). The stan-dard identification condition applies, that is, the predictorsof mit1 are not exactly the same as the predictors of mit2.This condition for identification is met in our empirical con-text because rank on the paid listings is different from therank on the organic listings for the same keyword in a giventime period.
Let us denote D and Eit as the conditional covariancematrix and mean vector of (�it1�it2�′, respectively, condi-tioning on values of ��it�it1�it2 %it )it�
′ and *. We useMetropolis–Hastings algorithm with a random walk chainto generate draws of �it = ��it1�it2�
′ (see Chib and Green-berg 1995, p. 330, method 1). Let ��p�
it denote the previousdraw, and then the next draw �
�n�it is given by
��n�it =�
�p�it +8
with the accepting probability � given by
min[exp�−1/2���n�
it −mit−Eit�′D−1��
�n�it −mit−Eit��l��
�n�it �
exp�−1/2���p�it −mit−Eit�
′D−1���p�it −mit−Eit��l��
�p�it �
1]
8 is a draw from multivariate Normal �00 05I�, where I isthe identity matrix.
2. Draw �i1 = ��i11�i12 �12i �
′.Let us denote d and eit as the variance and mean of �it1,
We use Metropolis–Hastings algorithm with a random walkchain to generate these draws (see Chib and Greenberg1995, p. 330, method 1). Let u�p�it1 denote the previous draw,and then the next draw u
�n�it1 is given by
u�n�it1 = u
�p�it1 +8
with the accepting probability � given by
min[exp�−1/2�u�n�it1 − uit1�
2�l�u�n�it1 �
exp�−1/2�u�p�it1 − uit1�2�l�u
�p�it1�
1]
8 is a draw from Normal�00 0025�.11. Draw uit2 similar to Step 10.12. Draw ci1 = �ci11 ci12�
′.Let us denote d and eij as the variance and mean of �it1,
conditional on the values of ��it1�it2�it1 %it )it�′ and *.
Let us denote d and eit as the variance and mean of %it ,conditional on the values of ��it1�it2�it1�it2 )it�
′ and *.
∼MVN�AB� A= B� 0/20 + x′w/d�−1
B= �1/20 + x′x/d�−1 0 = 0 and 2
0 = 100
24. Draw &i similar to Step 20.25. Draw & similar to Step 21.26. Draw 2
& similar to Step 22.27. Draw ' = �'1 '2 '3 '4 '5 '6�
′ similar to Step 23.28. Draw �i similar to Step 20.29. Draw �� similar to Step 21.
30. Draw 2� similar to Step 22.
31. Draw �= ��1�2�3�4�′ similar to Step 23.
32. Draw *.Let fit = ��it�it1�it2�it1�it2 %it )it�
′,
*∼ IW
(∑i
∑t
fitf′it +Q0N + q0
)
Q0 = 10I and q0 = 10 K = no. of observations
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